Efecto de las alteraciones de la normalidad sobre pruebas de comparación de medias paramétricas y no paramétricas

Abstract

The objective of this work was to determine the effect of alterations in normality in comparison tests of means, by estimating their Type I Error Probability (TIEP) and Power. For this, a simulation algorithm based on Monte Carlo was created, which estimated the TIEP as the proportion of rejections of the null hypothesis when it is true, and the Power as the proportion of rejections of the null hypothesis when it is false. To obtain the different measurable contaminations of normality in the samples, the Fleishman method was used. The results showed that when there is normality, the robustness of the parametric tests is better than their non-parametric alternatives, which was theoretically expected. In the event of alterations in normality, the TIEP of the parametric tests were better controlled than their non-parametric alternatives, all this up to certain levels of contamination, depending on the level at which they are still robust, the number of means to be compared and the sample sizes. In general, the TIEP of the parametric tests is highly variable, while the TIEP of the non-parametric tests remains constant. The Power of the parametric tests was better than that of their non-parametric alternatives, this also up to a certain degree of contamination of normality, however, when the sample sizes were large, the Power of both the parametric and non-parametric tests presented similar values, close to or equal to one. This work gives a vision of the correct use of means comparison tests in different scenarios of non-normality, sample size and number of treatments to be compared, it is suggested that these results should be applied in inferential analysis, which will lead to correct decision making.